Landau and his School

John Ziman

Name the greatest Russian physicist of this century. The public vote would go for Andrei Sakharov – but for moral stature rather than for contributions to knowledge. A generation ago, Pyotr Kapitza would have been supported by many, in the mistaken belief that he was the master mind behind the Russian Bomb. Among physicists, however, Ley Davidovitch Landau would stand preeminent. He ought, by rights, to be still with us, for he was born in 1908: but a ghastly car accident in 1962 destroyed his intellectual powers and in 1968 he died.

Perhaps he does not rank in the public mind with the top dozen theoretical physicists of our times because, as he himself admitted ruefully, ‘I was born a bit too late,’ thus missing the ‘Golden Age’ of the late 1920s, when all physics was being rebuilt from the ground up. But then again, he always insisted that it was sheer vanity to tackle only the most ‘important’ problems of science, so there is no saying whether he would have invented quantum mechanics and won that sort of fame.

Perhaps one has to accept that he was, above all, a paragon of the professionals. His Nobel Prize citation, in 1962, was ‘for pioneering theories for condensed matter, especially liquid helium’. Anna Livanova devotes half of her book to a most lucid elementary account of the theory of superfluidity of liquid helium, bringing the general reader as near as words can convey to an appreciation of this magical phenomenon and the wizardry he displayed in explaining it. And this was only one of the ‘Ten Commandments of Landau’ – a tablet presented to him on his 50th birthday, engraved with the famous formulae which he contributed to quantum theory, thermodynamics, magnetism, superconductivity, nuclear physics and the theory of elementary particles. His range within theoretical physics was unrestricted: his knowledge and creativity affected every branch of the subject. Very little of this work has come to the outer surface of science, in the form of useful hardware or disconcerting philosophy, but that is because theoretical physics is, by its very nature, an esoteric activity which is conducted in its own dimensions of the intellect, in its own particular language. Landau’s scientific thrusts were always directed at the central core of the subject, where only other theoretical physicists could fully appreciate their sharpness, precision and force.

The language of theoretical physics is, of course, mathematics, of which Landau was a master. Indeed, like every top professional, in performance he was oblivious to mere ‘technique’, which he had already transcended. There is a deceptive simplicity about the arguments of his papers, as if, somehow, everything followed naturally and inevitably from the basic physical laws. This apparently intuitive approach concealed a deep understanding of the mathematical inwardness of the situation, which few other physicists could adequately grasp. What we all admired about his scientific work was its unity – of mathematical formulae with physical concepts, of theoretical hypothesis with experimental fact, of romantic imagination with classical rigour. It was eclectic – and yet all of a piece.

I wish I could communicate to a wider public the special quality of Landau’s scientific achievements: but it is a bit like trying to express an appreciation of Mozart to the tone-deaf. One can get no closer than the mystical generalities by which Herman Hesse hinted at the nature of the glass bead game. Can one grasp more from his scientific personality, of which Anna Livanova gives such an evocative picture? Many great scientists, like many great artists and writers, appear, so to speak, quite inconsistent with their creations. This was not the case with Landau: he exercised his mind as brilliantly in discourse as in his own counsel, and was as influential as a teacher as in his published papers. The ‘School of Landau’, which he started at the age of 25, and unsparingly sustained thereafter, may have been his greatest achievement.

It was certainly a remarkable institution. There was no public qualification for admission. One just had to satisfy Landau personally that one had reached his ‘theoretical minimum’ – that is to say, that one knew all of theoretical physics sufficiently well to solve any problem he wanted to set! The informality of the arrangements – a telephone call to ask for a test on one of the topics, a quiet room in which to struggle with it – belied the rigour with which these examinations were relentlessly conducted. Even for a brilliant student, it took several years of intense effort to achieve the required standard: over the whole period from 1933 to 1961, only 43 candidates (in the whole of Russia) were successful. It is not surprising that at least seven are now members of the Soviet Academy of Sciences.

For the rest of us, all over the world, some idea of the scope of the theoretical minimum can only be got at second hand, from the encyclopedic Course of Theoretical Physics – another of Landau’s unique contributions to science. In fact, like almost all his published work, these many volumes were not actually written by Landau: he merely contributed the ideas, the mathematical proofs, the new formulations, and continual deep criticism, to manuscripts written and rewritten by his selflessly devoted co-author Evgeny Lifshitz – an accomplished physicist in his own right. It seems that he never read anything for himself either, relying on his students and colleagues to tell him exactly what they had done or what was worth noticing in the literature.

What went on inside the ‘School of Landau’? The key institution was the weekly Seminar – every Thursday at 11 a.m. on the dot – where pupils or visitors explained their own or other new work to the group. A theoretical physics seminar is an oven, where bright ideas get properly baked by collective criticism – or they frizzle to nothing. This particular audience was trained to be uninhibitedly scathing of every apparent imperfection, whether of exposition or logic. The atmosphere was informal, yet there was never any doubt that ‘Dau’ (as he was known to his intimates) was in complete command of the subject and the proceedings. Landau probably picked up this way of focusing individual opinions into a collective understanding from the year he spent attending Niels Bohr’s Seminar in Copenhagen, in 1929, when he was just 20. But he was much tougher and more aggressive than Bohr, and everything that went on in his research school was more deeply marked with his personal scientific style and preferences.

The central principle of his teaching was respect for convincing argument. There could be no half-truths in physics; the results had to follow from the premises, the theory had to fit the experiments, there must be no hazy steps in the mathematical analysis: otherwise it could be dismissed al once as ‘pathology’. Theoretical physics is the sort of science where these principles are prime virtues, provided that they are combined with wide knowledge and deep understanding of just what mathematical arguments and experimental facts might be brought to bear upon the point in question. Landau selected pupils with talents consistent with his own style of thought, and instilled these principles into them to the extent that they could be frank and free and democratic with him and one another. The morale of this élite scientific group can still be detected as a positive force in Russian science.

Nevertheless, he was damnably intolerant. A first impression of ‘pathology’, in an idea or a person, might never be overcome. Only a genius, who seldom made serious mistakes, could be forgiven such absolutism in his preferences. Even Landau could be disastrously wrong. Anna Livanova does not mention the manuscript paper by I.S. Shapiro, which Landau would not approve for publication in 1956. A few months later, Lee and Yang arrived at the same idea about the conservation of parity, for which they were soon awarded a Nobel Prize. And for lesser minds the completeness and coherence claimed for his Course of Theoretical Physics opens doors towards academicism. Landau’s scorn for pure mathematics tended to close the minds of his pupils to novel methods and concepts which were not already within the ‘minimum’ of theoretical physics.

This absolute confidence in his own judgment was only made tolerable by his absolute integrity and honesty. Landau was never an ‘easy’ man, in himself or with others. Although there is ample evidence of his sympathy with the problems of others – especially schoolchildren and aspiring students – he evidently had no capacity for empathy except in purely scientific matters. Despite his outward openness and directness, personal affairs were taboo in conversation with his pupils. ‘This is an item in your biography,’ he would say. Anna Livanova’s biographical memoir of him lacks many such items. He practised a superficial unpretentiousness in clothes and social manners, but never concealed from lesser mortals his disdain for their follies or weaknesses. He was driven from Leningrad and Kharkhov by irate seniors whose vanity he had pricked. It was the brave and wise Kapitza who took him into his Institute in Moscow, and provided a protected environment in which he could thrive. Although we talk of the ‘School of Landau’, it was not until after his death that an independent L.D. Landau Institute of Theoretical Physics was actually created.

And in spite of the fact that he was entirely dedicated to physics, to the pursuit of knowledge in its most refined and superhuman form, he cannot be separated from the background of his country, his people and his era. Anna Livanova refers to ‘one very burdensome year’ in which Landau reconstructed for himself, without paper and pencil, the theory of shock waves. I had to turn once more to the valuable little memoir by F. Janouch (published in March 1979 by CERN) to check that this was 1938, when Landau was thrown into prison, and would have been yet another innocent and irreplaceable victim of Stalin’s purges had not Kapitza, with the utmost courage, and Bohr, with infinite tact, interceded for him. It should not be altogether ignored, however, that in 1954 he was made a Hero of Socialist Labour – presumably for secret work, during and after the war, not unconnected with nuclear weapons and other explosive devices. To our eyes, now, he belongs unmistakably to world science, but he had little direct experience of life outside Russia, and was no ‘cosmopolitan’ in his attitudes.

In the circumstances of Soviet life, it is not surprising that he kept his own counsel on political issues. But what did he really think about the human condition? The deficiency of evidence is tantalising in someone with such a powerful, alert understanding, so confident in his opinions. He was, apparently, interested in the private lives of his friends and always ready with advice on how to solve their problems. But that was precisely how he saw the vicissitudes of life – as ‘problems’ to be scrupulously analysed and solved. Like some (but not all) very able scientists, he was a scientistic fundamentalist: he derived so much confidence from the power of scientific argument in its own sphere that he was convinced that it could be applied to every other.

Or was this extreme rationalism, with its denigration of all emotional considerations, simply the attempt of a very determined person to keep control of his own feelings? He believed that ‘every person should and must be happy. That is his duty to himself, to life and, if you will, to society.’ In his own work, it is clear enough what he meant – and although his biographers refer only perfunctorily to his marriage there is ample independent gossip about his ‘girls’. It seems, however, that he did not appreciate for himself many of the things that make other people happy. It would be absurd to suggest that a person of such transcendental genius dedicated himself to science because of this fundamental deficiency in his own personality: yet I have noticed the same trait in other theoretical physicists and mathematicians of lesser stature. He was the most perfect, most complete, and yet most sincerely admired and loved, example of a not unfamiliar human type.

Most of this comes out very clearly and sympathetically in this little book. But one major factor is missing. Look at his name. Lev Davidovitch Landau was not just a Russian: like many of his brightest pupils, he was also a Jew. Was he really ‘born too late’? Had he been a student in the 1950s, he might not have found a patron such as Kapitza to protect his acerbic intelligence from jealous enemies. Were he an applicant for admission to a Russian university now, he would have to surmount formidable barriers of officially-sponsored anti-semitic prejudice. I am told by a member of the Landau Institute that they have recently managed to find a post for another such brilliant young Jewish theoretician – but who knows whether Landau himself might not have ended up as a factory book-keeper or an immigrant in Israel. Like many Russian Jews of his generation, he cannot have been unaware that science was one of the few careers that were then open to their talents. Does this explain their exaggerated attachment to pure science, as if ‘physics’ were an end in itself, less a philosophical exercise than a self-justifying religion? This question is worth asking, because the life and work of L.D. Landau exemplifies the traditional ethic of pure science to the highest, despite the morally bankrupt, politically vicious and socially corrupt environment in which history had placed him. He did not, like Sakharov, stand up against infamy, but he stood uncompromisingly for truth.